Three-dimensional image reconstruction from complete projections

Three-dimensional medical image reconstruction for both transmission and emission tomography has traditionally decomposed the problem into a set of two-dimensional reconstructions on parallel transverse sections. There is, however, increasing interest in reconstructing projection data directly in three dimensions. For emission tomography in particular, such a reconstruction procedure would clearly make more efficient use of the available photon flux. In the past few years, a number of authors have studied the problems associated with full three-dimensional reconstruction, especially in the case of positron tomography where three-dimensional reconstruction is likely to offer the greatest benefits. While most approaches follow that of filtered backprojection, the relationship between the various filters that have been proposed is far from evident. This paper clarifies this relationship by analysing and generalising the different classes of published filters and establishes the properties and characteristics of a general solution to the three-dimensional reconstruction problem. Some guidelines are suggested for the choice of an appropriate filter in a given situation.